How Does Inserting a Dielectric Affect Capacitance and Potential?

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Homework Help Overview

The discussion revolves around the effects of inserting a dielectric on capacitance and potential in a capacitor setup. Participants are exploring the relationship between capacitance, energy, and force as a function of a variable x, while questioning the implications of different dielectric constants.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to derive expressions for capacitance and energy as functions of x. There are questions about the capacitance at specific points, particularly at x=0, and discussions about the implications of different dielectric materials.

Discussion Status

The discussion is ongoing, with participants raising questions about the assumptions made regarding the area and the dielectric's effect on capacitance. Some guidance has been offered regarding the need to draw equivalent circuits, but there is no explicit consensus on the correct expressions or interpretations yet.

Contextual Notes

There are uncertainties regarding the initial conditions of the capacitor and the configuration of the dielectrics involved. Participants are also navigating through the implications of their assumptions about the area and dielectric constants.

Arman777
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The Attempt at a Solution


I couldn't find the V(x).I don't know ho to write the equation.I think that it will be constant cause potential betwwen two plates should be constant... ?
 
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What is the energy in the capacitor as a function of x?
In other words, what is the capacitance as a function of x?
How is force related to this energy?
 
cnh1995 said:
What is the energy in the capacitor as a function of x?
In other words, what is the capacitance as a function of x?
How is force related to this energy?
##C_{eq}=(K+1)ε_0 \frac {xb} {d}## ? or maybe
##C=Kε_0 \frac {xb} {d}##
 
Arman777 said:
##C_{eq}=(K+1)ε_0 \frac {xb} {d}## ? or maybe
##C=Kε_0 \frac {xb} {d}##
I don't know the exact expression as I myself haven't worked it out yet, but check the answer at x=0. Is the capacitance zero at x=0?
 
cnh1995 said:
I don't know the exact expression as I myself haven't worked it out yet, but check the answer at x=0. Is the capacitance zero at x=0?
Yeah its
 
Arman777 said:
Yeah its
No, it isn't.
What is the capacitance for x=0?
 
cnh1995 said:
No, it isn't.
What is the capacitance for x=0?
there's no area when x=0
 
Arman777 said:
there's no area when x=0
How is this possible? Which area is considered for calculation of capacitance?
 
cnh1995 said:
How is this possible? Which area is considered for calculation of capacitance?
You are taking a-x I am just x
 
  • #10
Arman777 said:
You are taking a-x I am just x
But that doesn't make the total capacitance zero. You need to draw the equivalent circuit and find the total capacitance as a function of x.
 
  • #11
cnh1995 said:
But that doesn't make the total capacitance zero. You need to draw the equivalent circuit and find the total capacitance as a function of x.
I didnt understand
 
  • #12
Arman777 said:
I didnt understand
What is the dielectric between the plates before the new dielectric (with constant k) is inserted?
What is the capacitance when the new dielectric is not inserted at all?
 

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